Question

What is the ratio of the velocity of neon (Ne) atoms to the velocity of krypton (Kr) atoms when both gases are at the same temperature

Answer 1

As you know, the velocity of a gas is calculated by \(\sf v=\large\sqrt{\frac{3RT}{M}}\).
The ratio of v of \(\sf Ne\) to v of \(\sf Kr\) is
\(\sf \large \frac{ v_{Ne} }{ v_{Kr} }=\Large \frac{ \sqrt{\frac{ 3RT }{ M_{Ne} }} }{ \sqrt{\frac{ 3RT }{ M_{Kr} }} }=\Large \sqrt{\frac{ \cancel {3RT} }{ M_{Ne} }} { \sqrt{\frac{ M_{Kr}}{\cancel { 3RT} }} }=\sqrt{\frac{M_{Kr}}{M_{Ne}}}\)